Optimal probabilistic dense coding schemes

Abstract

Dense coding with non-maximally entangled states has been investigated in many different scenarios. We revisit this problem for protocols adopting the standard encoding scheme. In this case, the set of possible classical messages cannot be perfectly distinguished due to the non-orthogonality of the quantum states carrying them. So far, the decoding process has been approached in two ways: (i) The message is always inferred, but with an associated (minimum) error; (ii) the message is inferred without error, but only sometimes; in case of failure, nothing else is done. Here, we generalize on these approaches and propose novel optimal probabilistic decoding schemes. The first uses quantum-state separation to increase the distinguishability of the messages with an optimal success probability. This scheme is shown to include (i) and (ii) as special cases and continuously interpolate between them, which enables the decoder to trade-off between the level of confidence desired to identify the received messages and the success probability for doing so. The second scheme, called multistage decoding, applies only for qudits (d-level quantum systems with d > 2) and consists of further attempts in the state identification process in case of failure in the first one. We show that this scheme is advantageous over (ii) as it increases the mutual information between the sender and receiver.

Enhanced discrimination of high-dimensional quantum states by concatenated optimal measurement strategies

“…tection theory [7,[12][13][14][15][16][17], but in practice it became viable only recently with the development of experimental techniques for preparation, manipulation, and measurement of high-dimensional quantum systems. In addition to its fundamental interest, recent studies show that this concatenation provides significant improvements in probabilistic realizations of protocols like teleportation [18], entanglement swapping [19], and dense coding [20]; it will also have impact on high-dimensional quantum cryptography [20].…”

One-shot conclusive multiport quantum dense coding capacities

“…in Refs. [24,41,43], in which a "standard encoding scheme" utilizing generalized Pauli operators have been used. Generalized Pauli operators are given by U mn = X m Z n , where X and Z are defined by their actions on the elements |l of an orthonormal basis of the Hilbert space C d :…”

“…There is a significant body of work on generalizations of the original DC protocol in which the unitary encoding at the sender's node is on a single copy of the state while the decoding process of the receiver involves multiple copies, and refer to them as the generalized DC protocols. See, e.g., [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. See also [42].…”

“…certain online transactions where both card verification value ("CVV") and one-time password ("OTP") are needed, and possessing any one is useless for the task. Previous works on probabilistic versions of the dense coding protocol can be found in [24,30,31,41,45], although none of the schemes include the stipulation of complete information transfer.…”

Enhanced discrimination of high-dimensional quantum states by concatenated optimal measurement strategies

“…The possibility of concatenating optimized measurements has been the subject of intense investigation in quantum detection theory [7,[12][13][14][15][16][17], but in practice it became viable only recently with the development of experimental techniques for preparation, manipulation, and measurement of high-dimensional quantum systems. In addition to its fundamental interest, recent studies show that this concatenation provides significant improvements in probabilistic realizations of protocols like teleportation [18], entanglement swapping [19], and dense coding [20]; it will also have impact on high-dimensional quantum cryptography [20].…”